Introduction Overview
This chapter focuses on the wide variety of species classified as acids and bases. The first part describes the Brønsted definition, in which an acid is a proton donor and a base is a proton acceptor. Proton transfer equilibria can be discussed quantitatively in terms of acidity constants, which measure the tendency for species to donate protons.
In the second part, we introduce the Lewis definition of acids and bases, which deals with reactions involving electron-pair sharing between a donor (the base) and an acceptor (the acid). This broadening enables us to extend our discussion to include species that do not contain protons and to reactions in nonprotic media.
The original distinction between acids and bases was based, hazardously, on criteria of taste and feel: acids were sour and bases felt soapy. A deeper chemical understanding emerged from Arrhenius's (1884) conception of an acid as a compound that produced hydrogen ions in water.
Formation of acid rain - a classic acid-base reaction
4.1 Brønsted Acidity
A Brønsted acid is a proton donor and a Brønsted base is a proton acceptor. A proton has no separate existence in chemistry and is always associated with other species. A simple representation of a hydrogen ion in water is as the hydronium ion, H₃O⁺.
Johannes Brønsted in Denmark and Thomas Lowry in England proposed (in 1923) that the essential feature of an acid-base reaction is the transfer of a hydrogen ion, H⁺, from one species to another. In this context, a hydrogen ion is often referred to as a proton.
Brønsted Acid:
A proton donor
Brønsted Base:
A proton acceptor
An example of a Brønsted acid is hydrogen fluoride, HF, which can donate a proton to another molecule, such as H₂O, when it dissolves in water:
An example of a Brønsted base is ammonia, NH₃, which can accept a proton from a proton donor:
Water is an example of an amphiprotic substance - a substance that can act as both a Brønsted acid and a Brønsted base.
O-H bond: 101 pm
H-O-H angle: 100-120°
Better representation of proton in water
(a) Conjugate Acids and Bases
When a species donates a proton, it becomes the conjugate base; when a species gains a proton, it becomes the conjugate acid. Conjugate acids and bases are in equilibrium in solution.
The general Brønsted equilibrium can be written as:
The species Base₁ is called the conjugate base of Acid₁, and Acid₂ is the conjugate acid of Base₂. Thus, F⁻ is the conjugate base of HF and H₃O⁺ is the conjugate acid of H₂O.
Identify the Brønsted acid and its conjugate base in the following reactions:
(a) HSO₄⁻(aq) + OH⁻(aq) → H₂O(l) + SO₄²⁻(aq)
(b) PO₄³⁻(aq) + H₂O(l) → HPO₄²⁻(aq) + OH⁻
Answer: (a) The hydrogensulfate ion, HSO₄⁻, transfers a proton to hydroxide; it is therefore the acid and the SO₄²⁻ ion produced is its conjugate base. (b) The H₂O molecule transfers a proton to the phosphate ion acting as a base; thus H₂O is the acid and the OH⁻ ion is its conjugate base.
(b) The Strengths of Brønsted Acids
The strength of a Brønsted acid is measured by its acidity constant, and the strength of a Brønsted base is measured by its basicity constant; the stronger the base, the weaker is its conjugate acid.
The concept of pH is fundamental:
The strength of a Brønsted acid in aqueous solution is expressed by its acidity constant (or 'acid ionization constant'), Kₐ:
A value Kₐ ≪ 1 implies that [HX] is large with respect to [X⁻], and so proton retention by the acid is favoured. The experimental value of Kₐ for hydrogen fluoride in water is 3.5 × 10⁻⁴, indicating that under normal conditions only a very small fraction of HF molecules are deprotonated.
The pH of 0.145 M CH₃COOH(aq) is 2.80. Calculate Kₐ for ethanoic acid.
Answer: The concentration of H₃O⁺ is obtained from the pH: [H₃O⁺] = 10⁻²·⁸⁰ = 1.6 × 10⁻³ mol dm⁻³. Each deprotonation event produces one H₃O⁺ ion and one CH₃CO₂⁻ ion, so [CH₃CO₂⁻] = [H₃O⁺]. The molar concentration of the remaining acid is (0.145 − 0.0016) = 0.143 mol dm⁻³.
This value corresponds to pKₐ = 4.77.
The basicity constant, Kb, is similarly defined:
The autoprotolysis constant of water is:
An important relationship links the strength of a base to its conjugate acid:
(c) Strong and Weak Acids and Bases
An acid or base is classified as either weak or strong depending on the size of its acidity constant.
- Strong acid: pKₐ < 0 (Kₐ > 1, usually Kₐ ≫ 1) - almost fully deprotonated in solution
- Weak acid: pKₐ > 0 (Kₐ < 1) - equilibrium favours nonionized acid
- Strong base: Almost fully protonated in water (e.g., O²⁻ → OH⁻)
- Weak base: Only partially protonated (e.g., NH₃)
The conjugate base of any strong acid is a weak base, because it is thermodynamically unfavourable for such a base to accept a proton.
(d) Polyprotic Acids
A polyprotic acid loses protons in succession, and successive deprotonations are progressively less favourable; a distribution diagram summarizes how the fraction of each species present depends on the pH of the solution.
For a diprotic acid like H₂S, there are two successive proton donations:
The decrease in Kₐ is consistent with an electrostatic model: in the second deprotonation, a proton must separate from a centre with one more negative charge than in the first deprotonation.
Distribution Diagram for Phosphoric Acid (H₃PO₄)
pKₐ₁ = 2.12, pKₐ₂ = 7.21, pKₐ₃ = 12.68
(e) Factors Governing Strengths of Brønsted Acids and Bases
Proton affinity is the negative of the gas-phase proton-gain enthalpy. The proton affinities of p-block conjugate bases decrease to the right along a period and down a group. Proton affinities are influenced by solvation, which stabilizes species carrying a charge.
The proton affinity, Aₚ, of A⁻ is given by:
Where:
- B(H−A) is the H−A bond dissociation enthalpy
- I(H) is the ionization energy of hydrogen
- Aₑ(A) is the electron affinity of A
The Born equation describes the Gibbs energy of solvation:
Table 4.1 Acidity Constants at 25°C
| Acid | HA | A⁻ | Kₐ | pKₐ |
|---|---|---|---|---|
| Hydriodic | HI | I⁻ | 10¹¹ | −11 |
| Perchloric | HClO₄ | ClO₄⁻ | 10¹⁰ | −10 |
| Hydrobromic | HBr | Br⁻ | 10⁹ | −9 |
| Hydrochloric | HCl | Cl⁻ | 10⁷ | −7 |
| Sulfuric | H₂SO₄ | HSO₄⁻ | 10² | −2 |
| Nitric | HNO₃ | NO₃⁻ | 10² | −2 |
| Hydronium ion | H₃O⁺ | H₂O | 1 | 0.0 |
| Phosphoric | H₃PO₄ | H₂PO₄⁻ | 7.5 × 10⁻³ | 2.12 |
| Hydrofluoric | HF | F⁻ | 3.5 × 10⁻⁴ | 3.45 |
| Ethanoic | CH₃COOH | CH₃CO₂⁻ | 1.74 × 10⁻⁵ | 4.76 |
| Carbonic | H₂CO₃ | HCO₃⁻ | 4.3 × 10⁻⁷ | 6.37 |
| Hydrogen sulfide | H₂S | HS⁻ | 9.1 × 10⁻⁸ | 7.04 |
| Ammonium ion | NH₄⁺ | NH₃ | 5.6 × 10⁻¹⁰ | 9.25 |
| Hydrocyanic | HCN | CN⁻ | 4.9 × 10⁻¹⁰ | 9.31 |
| Hydrogensulfide ion | HS⁻ | S²⁻ | 1.1 × 10⁻¹⁹ | 19 |
4.2-4.5 Characteristics of Brønsted Acids
Aqua acids, hydroxoacids, and oxoacids are typical of specific regions of the periodic table.
There are three classes of acids to consider:
Acidic proton on coordinated water molecule
Acidic proton on hydroxyl group without neighboring oxo group
Acidic proton on hydroxyl group with oxo group attached
The strengths of aqua acids typically increase with increasing positive charge of the central metal ion and with decreasing ionic radius; exceptions are commonly due to the effects of covalent bonding.
The acidity should increase with increasing z (charge) and with decreasing r₊ (radius). Small, highly charged cations that are not easily polarized are hard and form complexes with small anions. Large cations are more polarizable and are soft.
Account for the trend in acidity: [Fe(OH₂)₆]²⁺ < [Fe(OH₂)₆]³⁺ < [Al(OH₂)₆]³⁺ ≈ [Hg(OH₂)]²⁺
Answer: The weakest acid is the Fe²⁺ complex on account of its relatively large ionic radius and low charge. The increase of charge to +3 increases the acid strength. The greater acidity of Al³⁺ can be explained by its smaller radius. The anomalous Hg²⁺ complex reflects the failure of an ionic model—there is large transfer of positive charge to oxygen as a result of covalent bonding.
The strengths of a series of oxoacids containing a specific central atom with a variable number of oxo and hydroxyl groups are summarized by Pauling's rules.
The trends can be systematized using two empirical rules (p = number of oxo groups, q = number of hydroxyl groups):
Pauling's Rule 1:
For the oxoacid OₚE(OH)q, pKₐ ≈ 8 − 5p
Pauling's Rule 2:
The successive pKₐ values of polyprotic acids (q > 1) increase by 5 units for each successive proton transfer.
| p value | Predicted pKₐ | Acid strength | Example |
|---|---|---|---|
| 0 | ≈ 8 | Very weak | HOCl (7.2) |
| 1 | ≈ 3 | Weak | H₂CO₃ (3.6) |
| 2 | ≈ −2 | Strong | H₂SO₄ (−1.9) |
| 3 | ≈ −7 | Very strong | HClO₄ (−10) |
Metallic elements typically form basic oxides; nonmetallic elements typically form acidic oxides. Amphoteric oxides react with both acids and bases.
Acidic Oxide:
An oxide that reacts with water to release protons or reacts with aqueous base
Basic Oxide:
An oxide to which a proton is transferred when it dissolves in water
Amphoteric Oxide:
An oxide that reacts with both acids and bases
Amphoterism is observed for lighter elements of Groups 2 and 13 (BeO, Al₂O₃, Ga₂O₃), d-block elements in high oxidation states (MoO₃, V₂O₅), and heavier elements of Groups 14 and 15 (SnO₂, Sb₂O₅).
Acids containing the OH group condense to form polyoxoanions; polycation formation from simple aqua cations occurs with the loss of H₂O. Polyoxoanions account for most of the mass of oxygen in the Earth's crust.
An example is the formation of the diphosphate ion from orthophosphate:
The formation of polyoxoanions is important for early d-block ions in their highest oxidation states, particularly V(V), Mo(VI), W(VI), and Cr(VI), for which the term 'polyoxometallates' is used.
Polyphosphates are biologically important—the key to energy exchange in metabolism is the hydrolysis of ATP to ADP:
4.6-4.7 Lewis Acidity
A Lewis acid is an electron-pair acceptor. A Lewis base is an electron-pair donor.
The Brønsted–Lowry theory of acids and bases focuses on proton transfer. A more general theory was introduced by G.N. Lewis in 1923. The fundamental reaction is the formation of a complex (or adduct), A–B, in which A and :B bond together by sharing the electron pair supplied by the base.
The Lewis acid provides an empty orbital (usually the LUMO), and the Lewis base provides a full orbital (usually the HOMO). The newly formed bonding orbital is populated by the two electrons supplied by the base.
4.6 Examples of Lewis Acids and Bases
Possibilities for Lewis acid behavior include:
- Incomplete octet: A molecule like B(CH₃)₃ can complete its octet by accepting an electron pair
- Metal cation: Can accept electron pairs in coordination compounds (e.g., [Co(OH₂)₆]²⁺)
- Rearranged valence electrons: CO₂ acts as Lewis acid when forming HCO₃⁻
- Expanded valence shell: Formation of [SiF₆]²⁻ from SiF₄ and 2F⁻
Identify the Lewis acids and bases in: (a) BrF₃ + F⁻ → BrF₄⁻, (b) KH + H₂O → KOH + H₂
Answer: (a) The acid BrF₃ accepts a pair of electrons from the base F⁻. (b) The saline hydride KH provides H⁻ which is a Lewis base that reacts with H₂O to drive out OH⁻, another Lewis base.
4.7 Group Characteristics of Lewis Acids
The ability of boron trihalides to act as Lewis acids generally increases in the order BF₃ < BCl₃ < BBr₃; aluminium halides are dimeric in the gas phase and are used as catalysts in solution.
This order is opposite to electronegativity expectations! The explanation is that halogen atoms in BX₃ form π bonds with the empty B2p orbital, and these must be disrupted for complex formation. Small F atoms form the strongest π bonds.
Aluminium chloride (Al₂Cl₆) is widely used as a Lewis acid catalyst for organic reactions like Friedel–Crafts alkylation:
Group 14: Silicon tetrahalides show acidity in order SiF₄ > SiCl₄ > SiBr₄ > SiI₄. Tin(II) chloride is both a Lewis acid and base!
Group 15: SbF₅ is one of the most widely studied Lewis acids and forms superacids with HF.
Group 16: SO₂ is both a Lewis acid and base. SO₃ is a strong Lewis acid (exothermic reaction with water → H₂SO₄).
Group 17: Br₂ and I₂ act as mild Lewis acids through their low-lying antibonding orbitals. The color change of iodine in different solvents demonstrates this—violet in nondonor solvents, brown in Lewis base solvents like acetone.
4.8-4.10 Reactions and Properties of Lewis Acids and Bases
Reactions of Lewis acids and bases are widespread in chemistry, industry, and biology. Examples include:
- Cement production (CaO + aluminosilicates)
- CO₂ removal using amine scrubbers
- Carbon monoxide toxicity (CO binding to Fe(II) in hemoglobin)
- Friedel–Crafts reactions in organic synthesis
4.8 Fundamental Types of Reaction
4.9 Hard and Soft Acids and Bases (HSAB)
Hard and soft acids and bases are identified empirically by the trends in stabilities of the complexes they form: hard acids tend to bind to hard bases and soft acids tend to bind to soft bases.
The two classes are identified by their opposite order of complex stabilities with halide ions:
- Hard acids: I⁻ < Br⁻ < Cl⁻ < F⁻ (stability increases)
- Soft acids: F⁻ < Cl⁻ < Br⁻ < I⁻ (stability increases)
Ionic bonding dominant
Acids:
- H⁺, Li⁺, Na⁺, K⁺
- Be²⁺, Mg²⁺, Ca²⁺
- Cr³⁺, Al³⁺, Fe³⁺
- BF₃, SO₃
Bases:
- F⁻, OH⁻, H₂O
- NH₃, CO₃²⁻
- NO₃⁻, SO₄²⁻
- PO₄³⁻, ClO₄⁻
Mixed character
Acids:
- Fe²⁺, Co²⁺, Ni²⁺
- Cu²⁺, Zn²⁺, Pb²⁺
- SO₂, BBr₃
Bases:
- NO₂⁻, SO₃²⁻
- Br⁻, N₃⁻, N₂
- C₆H₅N (pyridine)
- SCN⁻ (N-bound)
Covalent bonding dominant
Acids:
- Cu⁺, Ag⁺, Au⁺
- Hg²⁺, Pt²⁺, Pd²⁺
- Cd²⁺, Tl⁺
- BH₃
Bases:
- H⁻, R⁻, CN⁻, CO
- I⁻, SCN⁻ (S-bound)
- R₃P, R₂S
- C₆H₆ (benzene)
The bonding between hard acids and bases is predominantly ionic or dipole-dipole. Soft acids and bases are more polarizable, so the interaction has more covalent character.
4.10 Thermodynamic Acidity Parameters (Drago-Wayland Equation)
The standard enthalpies of complex formation are reproduced by the E and C parameters of the Drago-Wayland equation that reflect the ionic and covalent contributions to the bond.
The parameters E and C represent 'electrostatic' and 'covalent' factors, respectively. This equation is useful for reactions in nonpolar solvents and gas phase, but is limited mainly to neutral molecules.
Calculated: ΔfH° = −[(21.1 × 2.79) + (3.31 × 7.98)] = −85.28 kJ mol⁻¹
Experimental: −84.7 kJ mol⁻¹ ✓
4.11-4.13 Nonaqueous Solvents
Not all inorganic chemistry takes place in aqueous media. The properties of acids and bases are significantly altered by using nonaqueous solvents.
4.11 Solvent Levelling
A solvent with a large autoprotolysis constant can be used to discriminate between a wide range of acid and base strengths.
Any Brønsted acid stronger than H₃O⁺ in water donates a proton to H₂O and forms H₃O⁺. Consequently, no acid significantly stronger than H₃O⁺ can remain protonated in water. This is called the levelling effect.
- Acids are levelled if pKₐ < 0 in the solvent
- Bases are levelled if pKₐ > pKsol in the solvent
- The discrimination window ranges from pKₐ = 0 to pKsol
Interactive pH Scale
Hover over the pH scale to see examples
4.12 The Solvent-System Definition
The solvent-system definition extends the Brønsted-Lowry definition to include species that do not participate in proton transfer.
For an aprotic solvent like bromine trifluoride:
- Acid: Any solute that increases the concentration of the cation (BrF₂⁺)
- Base: Any solute that increases the concentration of the anion (BrF₄⁻)
4.13 Solvents as Acids and Bases
Dissolves alkali metals to give blue solutions with solvated electrons
Conjugate base is HF₂⁻; only very strong acids function as acids in HF
Complex autoionization; generates NO₂⁺ for nitration reactions
Wide discrimination window; hard (O) and soft (S) donor
Polar, nonvolatile; can provide very high concentrations of Lewis acids
Low viscosity, nonflammable; used for decaffeination and green chemistry
4.14-4.15 Applications of Acid-Base Chemistry
4.14 Superacids and Superbases
Superacids are more efficient proton donors than anhydrous sulfuric acid. Superbases are more efficient proton acceptors than the hydroxide ion.
Superacids are formed when a powerful Lewis acid is dissolved in a powerful Brønsted acid. They can be up to 10¹⁸ times more acidic than H₂SO₄.
An equimolar mixture of SbF₅ and HSO₃F is known as "magic acid", named for its ability to dissolve candle wax. Superacids have been used to observe reactive cations such as S₈²⁺, H₃O₂⁺, Xe₂⁺, and HCO⁺.
Superbases are usually salts of Group 1 and 2 cations with small, highly charged anions:
4.15 Heterogeneous Acid-Base Reactions
The surfaces of many catalytic materials and minerals have Brønsted and Lewis acid sites.
Surface acids (solids with high surface area and Lewis acid sites) are used as catalysts in the petrochemical industry. The most well-known class is zeolites, which are widely used as environmentally benign heterogeneous catalysts.
- Silica surfaces: Moderate Brønsted acidity (similar to acetic acid)
- Aluminosilicates: Strong Brønsted and Lewis acid sites
- Solid acids: Used in green chemistry to replace hazardous liquid acids
Surface modification reactions use Brønsted acid sites:
This procedure expands the range of stationary phases for chromatography and can be used to treat glassware for proton-sensitive compounds.
Summary Key Concepts
Brønsted Theory
- ✓ Acids donate protons
- ✓ Bases accept protons
- ✓ Kₐ and pKₐ measure acid strength
- ✓ KₐKb = Kw for conjugate pairs
Lewis Theory
- ✓ Acids accept electron pairs
- ✓ Bases donate electron pairs
- ✓ Forms complexes/adducts
- ✓ Applies to aprotic systems
HSAB Principle
- ✓ Hard acids prefer hard bases
- ✓ Soft acids prefer soft bases
- ✓ Hard = ionic bonding
- ✓ Soft = covalent bonding
Solvent Effects
- ✓ Levelling limits acid/base range
- ✓ Discrimination window = 0 to pKsol
- ✓ Superacids > H₂SO₄
- ✓ Superbases > OH⁻